EVALUATION E(exp(∫0th(s)dx(s)) ON ANALOGUE OF WIENER MEASURE SPACE

• Journal title : Honam Mathematical Journal
• Volume 32, Issue 3,  2010, pp.441-451
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2010.32.3.441
Title & Authors
EVALUATION E(exp(∫0th(s)dx(s)) ON ANALOGUE OF WIENER MEASURE SPACE
Park, Yeon-Hee;

Abstract
In this paper we evaluate the analogue of Wiener integral $\small{{\int\limits}_{C[0,t]}x(t_1){\cdots}x(t_n)d\omega_\rho(x)}$ where 0 = $\small{t_0}$ < $\small{t_1}$ $\small{\cdots}$ < $\small{t_n}$ $\small{\leq}$ t and the Paley-Wiener-Zygmund integral $\small{{\int\limits}_{C[0,t}$$\small{]}$$\small{}}$ exp $\small{({\int\limits}_0^t h(s)\tilde{d}x(s))d\omega_\rho(x)}$ is the analogue of Wiener measure space.
Keywords
analogue of Wiener measure;
Language
English
Cited by
1.
Analogues of Conditional Wiener Integrals with Drift and Initial Distribution on a Function Space, Abstract and Applied Analysis, 2014, 2014, 1
References
1.
Robert G. Bartle, The Elements of Real Analysis, John Wieley & Sons. Inc., 1976.

2.
D.L.,Cohn, Measure theory, Birkhauser, Boston, 1980.

3.
J. Diestel, and J.J. Uhl, Vecter measures, Mathematical Survey, No. 15, A. M. S., 1977.

4.
Parthasarathy, K.R., Probability measures on metric spaces, Academic Press, New York, 1967.

5.
K.S.Ryu and M.K.Im, A measure-valued analogue of Wiener measure and the measure-valued Feynman-Kac formula, Trans. Amer. Math. Sec., vol. 354, no. 12, 2002, 4921-4951.

6.
K.S.Ryu and M.K.Im, An analogue of Wiener measure and its applications, J. Korean Math .Sec., 39. 2002, no. 5, 801-819.

7.
K.S.Ryu and M.K.Im, The measure-valued Dyson series and its stability theorem, J. Korean Math. Soc., 43. 2006, no. 3, 461-489.

8.
K.S.Ryu and M.K.Im and K.S.Choi, Survey of the Theories for Analogue of Wiener Measure Space, Interdisciplinary Information Sciences Vol. 15, No.3, 2009, 319-337.

9.
K.S.Ryu The Generalized Fernique's Theorem for Analogue of Wiener Measure Space, J. Chungcheong Math. Soc., Vol. 22. No. 4, 2009, 743-748.

10.
Yeh, J., Stochastic processes and the Wiener Integral, Marcel Deckker, New York, 1973.